effects of cyclic freezing and thawing on the shear
TRANSCRIPT
Effects of Cyclic Freezing and Thawing on the ShearBehaviors of an Expansive Soil under a Wide Rangeof Stress LevelsWei-lie Zou
Wuhan UniversityZhong Han ( [email protected] )
Wuhan University https://orcid.org/0000-0002-8801-6503Gui-tao Zhao
Wuhan UniversityKewei Fan
Wuhan UniversitySai K. Vanapalli
University of OttawaXie-qun Wang
Wuhan University of Technology
Research Article
Keywords: Expansive soil, Freeze-thaw, Microstructure, Volumetric change, Shear behavior
Posted Date: June 3rd, 2021
DOI: https://doi.org/10.21203/rs.3.rs-507911/v1
License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
Version of Record: A version of this preprint was published at Environmental Earth Sciences on January25th, 2022. See the published version at https://doi.org/10.1007/s12665-022-10190-6.
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Effects of cyclic freezing and thawing on the shear behaviors of an 3
expansive soil under a wide range of stress levels 4
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Wei-lie Zou1,2,3, Zhong Han2,3*, Gui-tao Zhao2,*, Ke-wei Fan2, 6
Sai K. Vanapalli4, Xie-qun Wang5 7
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1Department of Civil Engineering, Xijing University, Xi’an, Shaanxi, 710123, China 9
2School of Civil Engineering, Wuhan University, Wuhan, Hubei, 430072, China 10
3Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering of the Ministry of 11
Education, Wuhan University, Wuhan, Hubei, 430072, China 12
4Department of Civil Engineering, University of Ottawa, Ottawa, ON, K1N6N5, Canada 13
5School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan, 14
Hubei, 430072, China 15
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*Corresponding authors: [email protected], [email protected] 18
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A manuscript submitted to Environmental Earth Sciences 23
for possible review and publication 24
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ABSTRACT 25
The focus of this paper is directed towards investigating the influence of multiple freeze-thaw 26
(FT) cycles on the stress-strain relationships during undrained shearing for an expansive soil 27
under a wide range of confining stresses (σc) from 0 to 300 kPa. Different numbers of FT 28
cycles were applied to compacted specimens. The influence of FT cycles on the soil’s 29
structure was investigated using mercury intrusion porosimetry (MIP) and scanning electron 30
microscope (SEM) tests. FT impacted specimens were subjected to consolidated undrained 31
(CU) shear tests with pore pressure measurement (σc = 10 to 300 kPa) and unconfined 32
compression (UC) tests (σc = 0 kPa) to derive the shearing stress-strain relationships and the 33
associated mechanical properties including (i) failure strength (qu), elastic modulus (Eu), 34
effective and apparent cohesion (c’ and c), and effective and apparent friction angle (ϕ’ and ϕ) 35
obtained from CU tests and (ii) qu and reloading modulus (E1%) and stress (Su1%) at 1% strain 36
obtained from UC tests. Testing results show that FT cycles mainly influence the soil’s 37
macropores with diameters between 5 and 250 microns. Cracks develop during FT cycles and 38
result in slight swelling which contributes to an increase in the global volume of the soil 39
specimens. There is a significant reduction in the investigated mechanical properties after FT 40
cycles. They typically achieve equilibrium after about 6 cycles. The shearing stress-strain 41
curves transits from strain-softening to strain-hardening as the confining stress increases. An 42
empirical model is developed to describe the strain-softening behavior of the specimens 43
under low confining stresses. The model is simple to use and well describes all stress-strain 44
curves obtained in this study that show strain-softening characteristics. 45
46
Keywords: Expansive soil; Freeze-thaw; Microstructure; Volumetric change; Shear behavior.47
3
Highlights: 48
• FT cycles destruct macropores and contribute to micro- and macrocracks 49
• The strength degradation associated with microstructural changes is explained 50
• The strain-softening behaviors under low stress levels of FT cycles are modeled51
4
1 INTRODUCTION 52
Expansive soils are typically referred to as problematic soils by geotechnical engineers 53
because of their significant swelling and shrinkage characteristics associated with variations 54
in their water content (Li et al. 1992; Nelson and Miller 1992; Zou et al. 2018). These soils 55
are widely distributed in many countries in the world, which include India, Israel, Canada, 56
Australia, China, and the USA (Jones and Holtz 1973; Ramana, 1993). The complex 57
variations in their engineering properties have a significant influence that results in damages 58
to the geotechnical infrastructures constructed on or adjacent to them. Expansive soils 59
typically lead to non-uniform settlement of structures, cracking of walls and pavements, and 60
landslides of expansive soil slope (Holtz and Gibbs 1956; Aitchison et al. 1973; Alonso et al. 61
1987; Chen, 1988; Schick et al. 1999; Miao et al. 2002; Tripathy et al. 2002; Glade, 2005; 62
Ajdari et al. 2013; Zhang et al. 2015; Massat et al. 2016; Zou et al. 2020). According to a 63
recent study by Adem and Vanapalli (2013), the economic losses caused by expansive soils 64
were estimated to be approximately several billion dollars in many countries in recent years. 65
66
There is a rapid development of geotechnical infrastructure in expansive soils regions in 67
China that are typically subjected to numerous freeze-thaw cycles annually (Lai et al. 2012; 68
Kong et al. 2018; Tang et al. 2018). A new large-scale water conveyance canal constructed in 69
Northeast China, which is 203 km in length, is an example of such an infrastructure in typical 70
weak and medium expansive soils (Xu et al. 2016). The expansive soils in this region are 71
subjected to periodic freeze-thaw (FT) cycles with fluctuations in the ground temperature. 72
Due to this reason, there is ice formation and the migration of water in the expansive soils 73
(Edwin and Anthony 1979, Liu et al. 2016), resulting in a change in the density and the 74
engineering properties, which include, coefficient of permeability, shear strength and 75
volumetric change (Qi et al. 2008; Aldaood et al. 2014; 2016; Zhang et al. 2015; Liu et al. 76
5
2017). There is evidence to show that these changes have contributed to numerous landslides 77
in the water conveyance canal (Xu et al. 2016; Zhang et al. 2018). 78
79
Expansive soils contain high quantities of swelling clay minerals such as montmorillonite and 80
illite that have a significant influence on the volumetric variations during cyclical moisture 81
content changes (Alonso et al. 1999; Tripathy et al. 2002). The volume change is typically 82
characterized by significant expansion and weakening upon wetting and shrinkage and 83
cracking upon drying, which cause extensive damages to the adjacent infrastructure and even 84
result in natural disasters (Holtz and Gibbs 1956; Berndt and Coughlan 1976; Chen and Ma 85
1987; Chen 1988; Lin and Cerato 2013; Gatabin et al. 2016; Liu et al. 2020). A significant 86
number of studies focused on the effect of drying-wetting cycles on the structural, volumetric, 87
and hydro-mechanical behaviors of expansive soils (Grant 1974; Albrecht and Benson 2001; 88
Cui et al. 2002; Alonso et al. 2005; Cuisinier and Masrouri 2005; Pires et al. 2008; 89
Nowamooz and Masrouri 2008; Ajdari et al. 2013; Wang et al. 2017). Also, several studies 90
have investigated the influence of freeze-thaw cycles on the mechanical behavior of various 91
soils, such as saline soil (Han et al. 2018), loess (Li et al. 2018), dispersive soil (Han et al. 92
2021), silty soil (Cui et al. 2014; Chen et al. 2019) and mine tailings (Liu et al. 2018). 93
However, due to the expansive soils’ complex deformation characteristics, the evolution of 94
engineering properties of expansive soils during FT cycles are more complex in comparison 95
to conventional soils. There are limited studies in the literature that address the effects of FT 96
cycles on the microstructure and mechanical behavior of expansive soils. In particular, the 97
effects of FT cycles on mechanical behaviors under low stress levels are not well understood. 98
99
In this study, the volumetric characteristics, the stress versus strain relationships, and shear 100
strength behaviors of an expansive soil collected from Northeastern China under the effects 101
6
of FT cycles were investigated. The investigated mechanical behaviors include (i) unconfined 102
compression strength and the unloading-reloading modulus, (ii) shear strength, elastic 103
modulus, and strength parameters (i.e. cohesion and internal friction angle) that were 104
obtained from consolidated undrained shear tests. Microstructural changes were derived from 105
mercury intrusion porosimetry (MIP) and scanning electron microscope (SEM) tests. Besides, 106
an empirical model is proposed to describe the strain-softening behavior of expansive soil 107
specimens under low confining pressures that can serve as a useful numerical tool. 108
109
2 EXPERIMENTAL INVESTIGATIONS 110
2.1 Materials 111
An expansive soil collected from Qiqihar, Heilongjiang, China is used for this research study. 112
The sampling site is a typical seasonally frozen region characterized by hot summer and cold 113
winter. The average temperature ranges from 23.1°C in summer to −18.6°C in winter. The 114
expansive soil was excavated from approximately 1m beneath the ground surface, and the 115
in-situ natural gravimetric water content (wn) and dry density (ρdn) of the sampled soil was 116
26.3% and 15.09 kN/m3, respectively. Physical index properties of the tested soil are 117
summarized in Table 1. 118
119
XRF tests were conducted to determine the chemical components of the soil. The major 120
chemical components and their contents by mass are SiO2, 60.48%; Al2O3, 18.53%; Fe2O3, 121
6.63%; K2O, 3.05%; CaO, 4%. XRD tests were conducted to reveal the mineral components 122
of the soil. The major minerals are Quartz, Illite, Albite, and Calcite. According to the 123
standard of GB 50112-2013 (Ministry of Housing and Urban-Rural Development, P.R. China, 124
2013) and the free swelling ratio of 67%, this soil is classified as moderately expansive soil. 125
126
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2.2 Specimen preparation and application of FT cycles 127
The collected expansive soil samples were air-dried, pulverized with a rubber mallet, and 128
then passed through a 2mm sieve to remove gravels and large size particles. To simulate the 129
field condition, the air-dried soil was wetted with water such that the natural water content of 130
26.3% is achieved. The moist soil was statically compacted at the natural dry density of 131
1540kg/m3 into cylindrical specimens (38mm in diameter and 76mm in height) for 132
microstructure investigations and triaxial tests. Compacted specimens were sealed in layers of 133
Saran wrap and stored in plastic containers for at least 72h at room temperature of 25±1°C to 134
ensure that water was evenly distributed within the specimens. 135
136
Specimens were subjected to freeze-thaw cycles in a closed-system condition. There is 137
limited or no moisture migration during freezing and thawing processes because of the 138
relatively low coefficient permeability of expansive soils, especially under unsaturated and 139
frozen conditions (Chamberlain 1973; Yarbasi et al. 2007; Lu et al. 2018). A temperature 140
chamber with a precision of ±0.05°C and a temperature range from 100°C to -40°C was used 141
to apply FT cycles. 142
143
During FT cycles, all specimens remain wrapped in Saran sheets and stored in plastic 144
containers which were firstly frozen at −20°C for at least 12h and then allowed to thaw at 145
20°C for another 12h. The temperature range was chosen following the local annual 146
temperature variation (i.e. −18.6°C to 23.1°C). A 12h period is considered enough for 147
achieving equilibrium conditions as small-size specimens are used in this study (Lu et al. 148
2019; Ding et al. 2020). Such freezing and thawing procedure was repeated until the 149
8
designated number of FT cycles (i.e. NFT = 0, 1, 4, 6, 10) was reached. 150
151
2.3 Measurement of volumetric change 152
To study the volumetric behavior of expansive soil specimens during FT cycles, the volume 153
measurements were performed on specimens after each freezing and thawing process. An 154
electronic Vernier caliper with an accuracy of 0.005mm was used to directly measure the 155
diameter and height of the specimens. Preliminary studies have shown that the volumetric 156
strain (ɛv) during FT cycles was found to be uniform in the homogenous soil specimens 157
which is consistent with the assumption of the uniform distribution of water phase in soil 158
mass and is widely used by various researchers (Zeng et al. 2018; Lu et al. 2019). Thus, 159
diameter (i.e. d1, d2, and d3) and height (i.e. h1, h2, and h3) measurements were taken at three 160
different cross-sections that are evenly distributed on the surface of the specimens. The 161
average values of diameter and height measurements were used to calculate the global 162
volume of the specimens and the void ratio (e) or volumetric strain (ɛv) – water content (w) 163
relationships. 164
165
2.4 MIP and SEM tests 166
To track the evolution of the microstructure of specimens upon freeze-thaw cycles, the 167
mercury intrusion porosimetry (MIP) tests and scanning electron microscopy (SEM) tests 168
were performed on untreated specimens and specimens subjected to 1, 4, 6, and 10 FT cycles. 169
MIP tests determine quantitatively the distribution and size of soil’s pores while SEM tests 170
capture the cross-section morphology of the microstructure. 171
172
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Approximately 2g of mass trimmed from test specimens subjected to different FT cycles were 173
collected for use in MIP and SEM tests. They were freeze-dried in liquid nitrogen to preserve 174
the soil structure and remove the pore water before testing. The trimmed specimens were then 175
subjected to MIP tests in a PoreMaster 33 porosimeter and SEM tests in an FEI Quanta 200 176
SEM testing system. 177
178
2.5 Determination of mechanical properties 179
A GDS static triaxial testing system (manufactured by GDS Instruments Ltd., Hampshire, 180
U.K., as shown in Figure 1), was utilized for the consolidated undrained (CU) triaxial 181
compression tests and unconfined compression (UC) tests to determine the mechanical 182
properties of expansive soil subjected to FT cycles. It should be noted that the UC tests were 183
performed on both saturated (specimens after achieving designed FT cycles were saturated 184
before performing the tests) and unsaturated specimens (specimens after achieving designed 185
FT cycles were directly used for tests), while CU tests were only performed on saturated 186
specimens. 187
188
Before performing the CU triaxial compression tests, the untreated specimens were subjected 189
to planned FT cycles and were vacuum saturated over a period of 24h. They were thereafter 190
transferred to the triaxial chamber where they were further subjected to back-pressure 191
saturated until the pore-water pressure parameter, B exceeds 0.90 (Kamruzzaman et al. 2009). 192
Afterward, the specimens were consolidated under seven different confining pressures (σc) of 193
10, 20, 30, 50, 100, 200, 300kPa. The consolidation process was assumed to have been 194
completed when the specimens’ volumetric changes leveled off and their excess pore water 195
10
pressure has dissipated. Finally, the specimens were sheared under undrained conditions at a 196
shear strain rate of 0.066%/min until the axial strain reached 20%. 197
198
The unconfined compression (UC) tests following the methodology suggested by Han and 199
Vanapalli (2017). This methodology involves an unloading-reloading loop starting at 1% 200
axial strain (ɛa) to determine the axial stress at ɛa =1% before the unloading process (i.e. Su1%) 201
and the reloading modulus at ɛa =1% (i.e. E1%). The unconfined compression strength (qu) 202
was determined after the specimens were loaded to failure. A loading and unloading rate of 203
1mm/min was adopted following the ASTM D2166-13 (2013) protocol. The Su1% and E1% are 204
elastic properties and qu indicates the unconfined shear strength of the specimens (Lee et al. 205
1997; Lu and Kaya 2013). Detailed discussions of the use of E1%, Su1%, and qu and testing 206
procedures of the revised UC tests are available in Lee et al. (1997) and Han and Vanapalli 207
(2017). Figure 2 shows the schematic diagram of the stress-strain relationship during the 208
revised UC tests and the determination of the E1%, Su1%, and qu. 209
210
3 TESTS RESULTS AND DISCUSSIONS 211
3.1 Volumetric characteristics 212
The volumetric strain (ɛv) of specimens during FT cycles can be defined using Eq. 1. 213
0 0/ 100%v NV V V (1) 214
where V0 is the initial volume of the untreated specimen, VN is the volume of the specimen 215
after experiencing N FT cycles. Positive ɛv indicates swelling while negative ɛv refers to 216
shrinkage. 217
218
11
The evolution of ɛv during 1, 4, 6, 10 FT cycles is shown in Figure 3. The volume change of 219
specimens with different NFT shows similar features (i) there is an increase in the ɛv (i.e. 220
expansion) during the freezing process and (ii) there is a decrease in the ɛv (i.e. shrinkage) 221
during the thawing process. The ɛv during initial several FT cycles are significant but its scale 222
reduces gradually with an increase in the NFT. The volumetric deformation behavior is elastic 223
after about 4 FT cycles, meaning that the non-recoverable ɛv becomes almost negligible when 224
NFT ≥ 4, which is consistent with the observations of other similar studies reported in the 225
literature (Viklander 1998; Wang et al., 2017; Zeng et al., 2018). FT cycles result in a slight 226
expansion of ɛv (ɛv = 1.2%) in the specimens’ volume after 10 FT cycles. 227
228
3.2 Evolution of soils’ microstructure 229
The MIP test results of specimens subjected to different FT cycles (NFT = 0, 1, 4, 6, 10) are 230
plotted in Figure 4. Related SEM images are shown in Figure 5. MIP results are presented in 231
the form of (i) cumulative intrusion (CI) curves (Figure 4a) and (ii) pore size distribution 232
(PSD) curves (Figure 4b). The CI curves are defined as the relationship between the intruded 233
mercury void ratio, eMIP (eMIP = Vm / Vs where Vm is the volume of intruded mercury and Vs is 234
the volume of the soil solids), and the pore diameter, d. The PSD curves are the derivatives of 235
CI curves (i.e. −δeMIP/δlogd versus logd relationships). 236
237
It is observed from Figure 4b that untreated specimens (NFT = 0) have a bimodal PSD curve 238
and with two dominant peaks: the peak of micro-pores at about 1.3μm and the peak of 239
macro-pores at about 30μm. This observation is consistent with the previous studies that the 240
as-compacted specimens usually show bimodal PSD curves (Wang et al, 2014; Burton et al, 241
2015). Macropores with diameters close to 30μm also can be observed in SEM images (see 242
Figure 5). 243
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244
For a better description of the microstructure’s evolution during FT histories, the CI and PSD 245
curves were separated into three zones (i.e. zones A, B, and C) by two boundaries which are 246
defined at 0.1μm and 5μm (see Figure 4). 0.1μm is chosen because all PSD curves converge 247
at the left of this threshold suggesting that these pores with diameters smaller than 0.1μm are 248
hard to be affected during FT cycles. 5μm is chosen as the delimiting boundary separating the 249
macro-pores and micro-pores in PSD curves of the tested soil, which is consistent with the 250
criterion proposed by Burton et al. (2015). 5μm is the turning point of PSD and CI curves 251
which refer to the beginning of the main population of micro-pores. 252
253
In order to quantitatively evaluate the variation of microstructures, the void ratio in zones A, 254
B, and C (denoted as ΔeMIP,A, ΔeMIP,B, ΔeMIP,C) are calculated by eMIP,A = eMIP,0.01 − eMIP,0.1, 255
eMIP,B = eMIP,0.1 − eMIP,5, eMIP,C = eMIP,5 where eMIP,N is the eMIP value at Nμm. The eMIP,0.01 is the 256
total void ratio intruded by mercury in the MIP tests (eMIP,0.01 = ΔeMIP,A + ΔeMIP,B + ΔeMIP,C). 257
The values of ΔeMIP,A, ΔeMIP,B, ΔeMIP,C and eMIP,0.01 are summarized in Table 2. 258
259
The following information can be derived from Figures 4 and 5 and Table 2: 260
(i) In Zone A, the FT cycles have a negligible effect on the microstructure as the shape of 261
CI and PSD curves remain unchanged and the calculated void ratio in this zone (i.e. 262
eMIP,A) is approximately the same after different FT cycles. 263
(ii) In Zone B, the eMIP,B decreases during FT cycles, such behavior suggests that some 264
micro-pores transformed into macro-pores due to the ice crystal formation during the 265
process of freezing. This is the result of irreversible frost-induced plastic deformation 266
of soil particles in the subsequent thawing process. The peak of the micro-pores in the 267
PSD curve shifts to the right, indicating a slight increase in the diameter of the 268
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dominant micro-pores. The frequency (i.e. −δeMIP/δlogd) corresponding to the peak of 269
the PSD curve, also decreases after FT cycles. 270
(iii) In Zone C, the eMIP,C increases during FT cycles, which confirms the transformation of 271
micro-pores to macro-pores. The peak of compaction-induced macro-pores in the PSD 272
curve of the initial untreated specimen disappears after a few FT cycles. However, a 273
new plateau in the range of 5-20μm develops which is stable during FT cycles. This 274
behavior also suggests that the compaction-induced macro-pores are unstable and prone 275
to collapse upon FT processes. 276
(iv) The evolution of microstructures during FT cycles observed in MIP results is consistent 277
with the SEM images. As shown in Figure 5, the variation of pores’ size and the 278
development of cracks induced by FT cycles can be easily observed. The cracks 279
induced by FT cycles segregate the soil particles and ultimately lead to a fragmented 280
soil structure. 281
282
3.3 Unconfined compressive strength properties 283
Figure 6 shows the stress-strain curves (i.e. axial stress, σ1 versus axial strain, ɛ1) obtained 284
from unconfined compression tests on saturated and unsaturated specimens with different FT 285
cycles (NFT = 0, 1, 4, 6, 10). The σ1-ɛ1 relationships show strain-softening characteristics. 286
With an increase in the FT cycles, axial strain at the peak strength (denoted as ɛp) increases 287
from approximately 2% of the untreated specimen to 3% after 10 FT cycles, for both 288
saturated and unsaturated specimens, and the pre-peak stress-strain curves tend to become flat. 289
The stress-strain curves of specimens with different NFT seem to have an identical residual 290
strength of approximately 15 and 30kPa for saturated and unsaturated specimens, respectively. 291
Comparing Figure 6(a) and (b), it can be observed that the saturated specimens have lower 292
residual strength and much lower peak strength than the unsaturated specimens, despite the 293
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consistent trends in stress-strain curves. 294
295
The evolution of qu, E1%, and Su1% values with NFT is shown in Figure 7. A power function 296
(Eq. 1) is used to describe the variation of qu, E1%, and Su1% with NFT under unconfined 297
compression. 298
0
1
1
N
N e
(1) 299
where Ω0 collectively represents the qu, E1%, and Su1% of untreated specimens, ΩN is the qu, 300
E1%, and Su1% after N cycles of treatment, α and β are model parameters, e = 2.7182. The 301
fitting curves are shown in Figure 7 and the values of fitting parameters (i.e. α, and β) are 302
summarized in Table 3. The variation in the qu, E1%, and Su1% with NFT is well described by 303
the proposed power function with R2 > 0.9. The following information can be derived from 304
Figure 7 and Table 3: 305
(i) The qu, E1%, and Su1% decrease with increasing NFT, especially during the initial two FT 306
cycles (NFT = 1, 4), which is followed by a slow decrease with further FT cycles and 307
reach equilibrium for unsaturated tests of approximately NFT = 6 and saturated tests of 308
NFT = 4, respectively. 309
(ii) The values of qu, E1%, and Su1% obtained from saturated specimens are much lower than 310
the ones of unsaturated specimens under the same NFT. For example, the qu, E1%, and Su1% 311
of saturated specimens decrease by 49.1%, 54.0%, and 71.4% from the initial values of 312
55kPa, 8.45MPa, and 49kPa for untreated specimens to 28kPa, 3.89MPa, and 14kPa after 313
10 FT cycles, respectively. For unsaturated specimens, the qu, E1%, and Su1% decrease 314
only by 46.0%, 45.2%, and 56.7% from 113kPa, 15.65MPa and 97kPa to 61kPa, 315
8.57MPa, and 42kPa, respectively. Thus, the decrease in the mechanical properties is 316
more significant during FT cycles when the moisture content is higher. 317
15
3.4 Shear strength and elastic modulus during consolidated undrained shearing 318
CU tests were conducted on specimens under seven confining stress levels (σc =10, 20, 30, 50, 319
100, 200, 300kPa) and with different NFT (NFT = 0, 1, 4, 6, 10) for comprehensive evaluation 320
of the influence of FT cycles on the mechanical properties of expansive soil. 321
322
The stress-strain relationships (i.e. deviator stress q versus axial strain ɛ1; q = σ1 − σc) 323
obtained from consolidated undrained triaxial shear tests under various confining pressures of 324
the specimens subjected to FT cycles shown in Figure 8. The untreated specimens and the 325
specimens subjected to FT cycles exhibit strain-softening behavior (see Figure 8) under low 326
confining pressures (i.e. 10, 20, and 30kPa). However, the strain-softening behavior gradually 327
decreases with increasing confining pressure. The stress-strain curves start to show a strain- 328
stabilization behavior when the confining pressure exceeds 50kPa and show a 329
strain-hardening behavior at a confining pressure of 100 and 300kPa (see Figure 8). The 330
shear strength (i.e. qu) is equal to the peak deviator stress for the specimens exhibiting 331
strain-softening characteristics. However, the shear strength is estimated at the axial strain of 332
15% for the specimens exhibiting strain stabilization or hardening characteristics (Zhang et al. 333
2015; Liu et al. 2018). Typical results of the failure strength due to FT cycles under low and 334
high confining pressures are given in Figure 9. 335
336
The shear strength (i.e. qu) for all specimens decreases with an increase in the NFT and 337
reaches an equilibrium after approximately 6 cycles regardless of the confining pressure (i.e. 338
σ3). A more significant reduction however was observed for low confining stress (i.e. σc = 10, 339
20, and 30kPa). According to Wang et al. (2007) and Tang et al. (2018), a more compacted 340
structure is formed due to the soil particle rearrangement associated with the closure of cracks 341
induced due to the influence FT cycles. 342
16
343
The elastic modulus (i.e. Eu) is an important parameter that reflects the ability of a soil to 344
resist deformation (Tang et al. 2018; Han et al. 2018). According to Lee et al. (1995), the 345
elastic modulus can be calculated using Eq. (2) from stress-strain curves: 346
1% 0
1% 0
u
q qqE
(2) 347
where ∆q and ∆ɛ are the increments of deviator stress and axial strain, respectively; q1% is the 348
deviator stress corresponding to an axial strain of 1% (i.e. ɛ1%), q0 is the initial deviator stress 349
corresponding to initial axial strain ɛ0. The results of Eu for specimens subjected to FT cycles 350
under various low and high confining pressures are given in Figure 10. 351
352
A significant reduction in the Eu with an increase in the NFT can be observed. Such behavior 353
is due to the modified micro-structures introduced by freeze-thaw cycles, which greatly 354
reduce the ability of specimens to resist elastic deformation. These observations are 355
consistent with the variations of qu that almost no appreciable decrease in the Eu was 356
observed after NFT = 6. 357
358
The effective and apparent cohesion (c’ and c, kPa) and the effective and apparent cohesion 359
internal fraction angle (ϕ’ and ϕ, °) under each confining pressure was separately determined 360
from the Mohr-Coulomb model (Eq. 3) to evaluate their evolutions with NFT. 361
1 3
2 cos 1 sin+
1 sin 1 sin
c
(3a) 362
1 3
2 cos 1 sin+
1 sin 1 sin
c
(3b) 363
The evolution of determined c’ and ϕ’ and c and ϕ with different NFT are summarized in 364
Figures 11 and 12, respectively. 365
17
366
Because of the particle rearrangement and compaction effects during the consolidation and 367
shearing processes, the effective and apparent cohesion (i.e. c’ and c) and internal friction 368
angle (i.e. ϕ’ and ϕ) exhibit a non-linear characteristic as the confining pressure increases. A 369
lower cohesion and higher internal friction angle were observed for lower confining pressures, 370
these results are consistent with the previous studies (Chen and Liu 1990; Jiang et al. 2003; 371
and Li and Cheng 2012). An obvious reduction was also observed in the shear strength 372
parameters c’ and ϕ’ with the increasing cycle number, NFT. Such a behavior can be attributed 373
to the influence of FT cycles that introduce cracks to soil structure (see Figure 5), which 374
reduce the integrity of soil particles that results in a reduction of their effective contacts. 375
376
The aforementioned power function (Eq. 1) was also used to describe the variation of qu, Eu, 377
c’ and ϕ’ and c and ϕ with different NFT under consolidated undrained shearing. The fitting 378
curves are shown in Figures 9, 10, 11, and 12, and the fitting parameters (i.e. α, and β) are 379
given in Table 4. 380
381
4 MODELLING STRESS-STRAIN BEHAVIORS 382
The strain stabilization and hardening behavior of specimens under high confining pressures 383
(i.e. σc = 50, 100, 200, 300kPa) can be described by the Duncan-Chang model (i.e. Eq. (4)) 384
and shown in Figure 8. 385
1
1
qa b
(4) 386
where ɑ and b are model parameters. According to Gutierrez et al. (2008), Moniz (2009), and 387
Ladd et al. (1977), 1/ɑ is the slope of the initial curve and equals the undrained elastic 388
modulus, Eu. 1/b is the ultimate deviator stress and indicates the undrained shear strength, qu. 389
Fitting parameters and R2 are summarised in Table 5. 390
18
391
Extending the concepts of the Duncan-Chang model, an empirical model Eq. (5) was 392
proposed to describe the strain-softening behavior of specimens subjected to different FT 393
cycles which are observed from CU and UC tests. 394
110 -1
1
ln 2.718 (10 / )m
nq
a b
(5) 395
where λ, κ, n, m, are model parameters. λ is related to the ratio of residual strength to peak 396
strength, κ, n, and m are the model parameters related to the axial strain at peak deviator 397
stress, the slope of descending portion of the stress-strain curves, and the axial strain at 398
residual deviator stress. 399
400
The fitting curves are shown in Figures 6 and 8 and fitting parameters are summarised in 401
Table 6 highlight good agreements between the measurements and the predictions. The 402
residual axial strain and corresponding residual deviator stress and the subsequent horizontal 403
section of stress-strain curves were well described. 404
405
5 CONCLUSIONS 406
In this paper, the influence of multiple FT cycles on the microstructure and mechanical 407
behaviors (including volumetric behavior, stress-strain behavior, shear strength parameters, 408
and elastic modulus during consolidated undrained shearing and shear strength and 409
unloading-reloading modulus during unconfined shearing) of an expansive soil was 410
investigated from experimental studies. The following observations and conclusions were 411
derived. 412
(i) The compaction-induced macro-structures are altered in the range of 5 to 250 microns 413
due to the influence of FT cycles. Besides, FT cycles introduce cracks into the soil 414
structure. It is important to note that FT cycles have a minor influence on the 415
19
micropores with diameters less than 5 microns. The experimental results suggest that 416
soil swelled during the FT cycles. The volumetric behaviors become elastic after 417
approximately 4 cycles during FT treatments. 418
(ii) The qu, E1%, and Su1% obtained from unconfined compression tests decrease 419
significantly with increasing NFT, especially during the initial two FT cycles, and reach 420
equilibrium after approximately 4 to 6 FT cycles. The values of qu, E1%, and Su1% for 421
saturated specimens are much smaller than the ones of unsaturated soil specimens for 422
the same NFT. 423
(iii) The qu, Eu, c, and ϕ obtained from consolidated undrained triaxial tests reduce due to 424
the influence of FT cycles; however, these are notably constant after 6 FT cycles. 425
426
A simple empirical model is developed to describe the strain-softening behavior of 427
stress-strain curves obtained from CU and UC shearing under low stress levels of specimens 428
undergoing 0, 1, 4, 10 FT cycles. The performance of this model is verified by the test results. 429
The model presented in this paper could be a useful tool in the numerical analysis of the 430
strain-softening behaviors that can be derived from the stress-strain curves. 431
DECLARATIONS 432 Acknowledgements 433 Authors gratefully acknowledge the funding received from the National Natural Science Foundation of China (Grant Nos. 434 51779191, and 51809199). 435 Competent of Interests 436 The authors declare that they have no known competing financial interests or personal relationships that could have appeared 437 to influence the work reported in this paper. 438 Authors' contributions 439 Wei-lie Zou: Supervision, Methodology, Formal analysis, Validation, Writing-original draft. 440 Zhong Han: Supervision, Conceptualization, Funding acquisition, Project administration, Writing-review & editing. 441 Gui-tao Zhao: Conceptualization, Methodology, Formal analysis, Writing-original draft. 442 Ke-wei Fan: Formal analysis, Writing-review & editing. 443 Sai K. Vanapalli: Methodology, Writing-review & editing. 444 Xie-qun Wang: Formal analysis, Writing-review & editing. 445 446 REFERENCES 447 Adem, H.H., Vanapalli, S.K., 2013. Constitutive modeling approach for estimating 1-D heave with respect to time for 448
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Figures
Figure 1
GDS triaxial apparatus for UC and CU tests
Figure 2
The schematic diagram of the stress-strain relationship and the determination of the E1%, Su1%, and quduring the revised UC tests
Figure 3
The volumetric variations of specimens during FT cyclic treatments
Figure 4
The (a) CI and (b) PSD curves of specimens after 0, 1, 4, 6 and 10 FT cycles
Figure 5
SEM images of (a) untreated specimens and specimens after 1, 4, 6, 10 FT cycles (b-e)
Figure 6
The UC stress-strain curves of specimens after 0, 1, 4, 6 and 10 FT cycles under (a) unsaturated and (b)saturated conditions
Figure 7
Variation of qu, E1%, and Su1% of specimens after 0, 1, 4, 6 and 10 FT cyclic treatments
Figure 8
The CU stress-strain relationships of specimens after 0, 1, 4, 6 and 10 FT cycles under various con�ningpressures (i.e. 10, 20, 30, 50, 100, 200 and 300kPa)
Figure 9
Evolution of Failure strengths obtained from CU tests with the increase of FT cycle numbers
Figure 10
Evolution of Elastic modulus of specimens obtained from CU tests with the increase of FT cycle numbers
Figure 11
Evolution of effective cohesions and effective friction angles obtained from CU tests with the increase ofFT cycle numbers
Figure 12
Evolution of apparent cohesions and apparent friction angles obtained from CU tests with the increase ofFT cycle numbers